Cabling procedure for the~colored HOMFLY polynomials
Teoretičeskaâ i matematičeskaâ fizika, Tome 178 (2014) no. 1, pp. 3-68
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We discuss using the cabling procedure to calculate colored HOMFLY polynomials. We describe how it can be used and how the projectors and $\mathcal R$-matrices needed for this procedure can be found. The constructed matrix expressions for the projectors and $\mathcal R$-matrices in the fundamental representation allow calculating the HOMFLY polynomial in an arbitrary representation for an arbitrary knot. The computational algorithm can be used for the knots and links with $|Q|m\le12$, where $m$ is the number of strands in a braid representation of the knot and $|Q|$ is the number of boxes in the Young diagram of the representation. We also discuss the justification of the cabling procedure from the group theory standpoint, deriving expressions for the fundamental $\mathcal R$-matrices and clarifying some conjectures formulated in previous papers.
Keywords:
Chern–Simons theory, knot theory, representation theory.
@article{TMF_2014_178_1_a0,
author = {A. S. Anokhina and A. A. Morozov},
title = {Cabling procedure for the~colored {HOMFLY} polynomials},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {3--68},
publisher = {mathdoc},
volume = {178},
number = {1},
year = {2014},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2014_178_1_a0/}
}
A. S. Anokhina; A. A. Morozov. Cabling procedure for the~colored HOMFLY polynomials. Teoretičeskaâ i matematičeskaâ fizika, Tome 178 (2014) no. 1, pp. 3-68. http://geodesic.mathdoc.fr/item/TMF_2014_178_1_a0/